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    Can logarithms be applied to Modular arithmetic

    I'm not sure of your background with modular arithmetic, so I'll just start small... We consider all numbers with the same remainder after dividing by n to be EQUIVALENT. For example, 2 = 5 = 8 = 11 = 300000000000002 = -1 mod 3. (Here, the "triple" bar sign would be better than the double bar...
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    System of coupled masses and springs homework

    (From an organizational standpoint, you could probably pick a more descriptive title...)
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    Trigonometric Equations find all solutions

    sec(3t) = 2 invert (flip) both sides cos(3t) = 1/2 Get a unit circle. Each point is of the form (cosine(angle), sine(angle)) We want the angles where cosine is 1/2. These angles are: π/3 and 5π/3 But since we have 3t, we include all solutions less than 6π. See the above reply for more details...
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    Advanced Functions,Exponential Functions

    Have you ever seen P = e^{rt} before? Usually, I would recommend exponential growth/decay for bacteria situations. Furthermore, "Doubling" and "halving" are very closely related!
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    Instructor doesn't know the answer to his own exam!

    What was the question ( question, so to speak)?
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    Unique abelian group of order n

    Since this was the first hit when I Googled my homework, I'll resurrect this thread with my thoughts. This holds trivially for prime numbers. Claim: For n "square-free", \mathbb{Z}_n is (up to isomorphism) the unique abelian group of order n. We extend the fact that \mathbb{Z}_{ab} \cong...
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    What is the absolute value of imaginary numbers, why not supernatural numbers?

    That is the beauty of math?!?! I wish someone had told me earlier... :cool:
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    What is the absolute value of imaginary numbers, why not supernatural numbers?

    I guess so! There was another "seemingly active thread" about closed form expressions that caught my eye today, as did the fact that some first-poster had resurrected it after years of inactivity...
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    Partition Function p(n)

    Too bad this guy doesn't come around anymore... I was just starting to like him! But seriously, forks. I do NOT know of a closed-form equation.
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    Differentiation of fraction

    Cancel a factor of h from top and bottom. Then let h -> 0 and you'll get \frac{-2}{x^2+2x+1} = \frac{-2}{(x + 1)^2} Later, when you learn "shortcuts" (i.e rules of differentiation that will be proven), this second form will look a lot more familiar.
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    Other answers to 1+1=2

    1 Point for calling out the flagrant bump. + 1 point for referencing the thread at the same time = the new constant named in your honor - "M"
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    Calculate arcsin(sin√5)

    TsAmE, I might add that Calculus *methods* are not appropriate for this problem (even though it might appear in a calc book/course). This is more about, as Mark44 has mentioned, coterminal angles and the domain of inverse trig functions. Some people have an easier time working with degrees at...
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    Help with Algebra

    Yeah, super disappointing. After finding critical points, you could use a sign chart to determine which are maxima and which are minima
  14. T

    Statistical probability to help with a crime

    Maybe you should invite the employees to a poker game...?!?!
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    Volume computation (from cross-sectional area)

    a. the base of the square isn't (y^2); it's (3-y^2).
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    Integration by Parts guidelines

    Sometimes when it looks like IBP isn't "working", you might need to do a little trick. Look up the integral of cosine times exp.
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    Post your Fall 2010 schedule!

    WOW. I'll just... be on my way... at the local community college! But seriously - that's awesome. What an opportunity (I speculate). As for me, I'm probably (just) taking Intro to Abstract II and Advanced Calc I.... with 2 part-time jobs and part-time parenting, there's only room left for...
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    Naive sign function for real numbers - challenge

    I will use the Lemmings suicide function. Then maybe this thread will truncate.
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    Paraboloid problem help

    The integral isn't correct. Your left-most integral bounds shouldn't have variables in it. Your right-most shouldn't have constants. You have used "z=" in two of the integrals, and "y=" in none.
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    Need something solving PROBLEM AHOY!

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    Need something solving PROBLEM AHOY!

    In real numbers, the problem is immediate: no linear combination of powers of e will ever equal -1. In complex numbers, L = W would make things a lot simpler, but that's trivial...
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    Basic algebra/Power laws equation

    Part a. x^n * 1/x^n = 1. To see this, notice that the left hand member is the same as x^n/x^n, and any nonzero number divided by itself is equal to one. Part b. x^n * x^-n = 1. To see this, use the rule of exponents that says "when multiplying like bases, add the exponents". So you will have...
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    How do I solve the integral x|x|dx?

    It was either THAT, or I was totally slamming Hurkyl (but not both)! I prefer the Socratic method to spoon-feeding.
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    How do I solve the integral x|x|dx?

    I wonder why Hurkyl didn't just say that in his reply... hmm... I guess he doesn't know how to do it... :eek:
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    Integral e^x.(lnx)dx=?

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    Integral of e^x/x

    Gave you WHAT answer? That article doesn't explain where the error is... Yes, you are having problems with the chain rule. If v = e^u, then dv/du = e^u, and dv = (e^u)du, which doesn't help solve the integral. If you wanted to take dv/dx, then that would equal (dv/du)*(du/dx), but that's not...
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    Integral of e^x/x

    How about googledocs???
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    Integral using partial fraction

    This is the kind of problem that you shouls do once, for whatever reason (!), and then use a computer for afterward! Good luck. wolframalpha can verify your results, in case you weren't aware of that resource.
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    Evaluating/Solving Logarithmic expressions/equations

    The difficulty in this prompts many to advise against exponentiating until exactly one log expression is on each side of the equality. But yeah, you can...
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    Solution to an eigenvalue problem ?

    Don't call me Shirley